Question

What is the completely factored form of x2 – 16xy + 64y2?

Answer 1

x² - 16xy + 64y²

= (x)² - 2(x)(8y) + (8y)²

= (x - 8y)²

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Answer 2

Step-by-step explanation:

Given:

$x^{2} -16xy+64y^{2}$

To find:

The factored form of $x^{2} -16xy+64y^{2}$

Solution:

Given that,  $x^{2} -16xy+64y^{2}$

Rewrite the term $(64)^2$ as $(8y)^2,$  

⇒ $x^{2} -16xy+(8y)^{2}$

And now, check if the middle term is more than twice the product of the squared numbers in the first and third terms.

$16xy=$ $2.x.(8y)$

Rewrite the given equation,

⇒ $x^2-2.x.(8y)+(8y)^2$

Use the perfect square formula for factor, $a^{2} -2ab+b^2=(a-b)^2$

Where, $a=x, b=8y$

⇒ $x^2-2.x.(8y)+(8y)^2=(x-8y)^2$

Hence the answer is,

$(x-8y)^2$ or $(x-8y) (x-8y)$

Answer:

The factored form $x^{2} -16xy+64y^{2}$ is $(x-8y) (x-8y).$